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In atmospheric science, several different expressions for the Richardson number are commonly used: the flux Richardson number (which is fundamental), the gradient Richardson number, and the bulk Richardson number. The flux Richardson number is the ratio of buoyant production (or suppression) of turbulence kinetic energy to the production of ...
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The Bulk Richardson Number (BRN) is a dimensionless number relating vertical stability and vertical wind shear (generally, stability divided by shear). It represents the ratio of thermally-produced turbulence and turbulence generated by vertical shear. Practically, its value determines whether convection is free or forced.
The Bulk Richardson Number (BRN) is an approximation of the Gradient Richardson number. [1] The BRN is a dimensionless ratio in meteorology related to the consumption of turbulence divided by the shear production (the generation of turbulence kinetic energy caused by wind shear) of turbulence.
Depending on the Richardson number, the boundary layer at the cold plate exhibits a lower velocity than the free stream, or even accelerates in the opposite direction. This second mixed convection case therefore experiences strong shear in the boundary layer and quickly transitions into a turbulent flow state.
The most important feature of baroclinic instability is that it exists even in the situation of rapid rotation (small Rossby number) and strong stable stratification (large Richardson's number) typically observed in the atmosphere. [citation needed] The energy source for baroclinic instability is the potential energy in the environmental flow.
The L and D subscripts indicate the length scale basis for the Grashof number. The transition to turbulent flow occurs in the range 10 8 < Gr L < 10 9 for natural convection from vertical flat plates. At higher Grashof numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is laminar, that is, in the range 10 3 ...
and consequently, the number of time steps grows also as a power law of the Reynolds number. One can estimate that the number of floating-point operations required to complete the simulation is proportional to the number of mesh points and the number of time steps, and in conclusion, the number of operations grows as R e 3 {\displaystyle ...